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Finding the Third Proportional to 6,434 and 8,409

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Solution

The third proportional to 6,434 and 8,409 is: 10,990.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,434 : 8,409 = 8,409 : x
  2. Step 2: Convert to fraction form
    6,434/8,409 = 8,409/x
  3. Step 3: Cross multiply
    6,434x = 8,409 × 8,409
  4. Step 4: Simplify right side
    6,434x = 70,711,281
  5. Step 5: Solve for x
    x = 70,711,281/6,434
  6. Step 6: Final answer
    x = 10,990.25

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.